Express your answer as a mixed number simplified to lowest terms. $18\dfrac{1}{6}-5\dfrac{8}{20} = {?}$
Solution: Simplify each fraction. $= {18\dfrac{1}{6}} - {5\dfrac{2}{5}}$ Find a common denominator for the fractions: $= {18\dfrac{5}{30}}-{5\dfrac{12}{30}}$ Convert ${18\dfrac{5}{30}}$ to ${17 + \dfrac{30}{30} + \dfrac{5}{30}}$ So the problem becomes: ${17\dfrac{35}{30}}-{5\dfrac{12}{30}}$ Separate the whole numbers from the fractional parts: $= {17} + {\dfrac{35}{30}} - {5} - {\dfrac{12}{30}}$ Bring the whole numbers together and the fractions together: $= {17} - {5} + {\dfrac{35}{30}} - {\dfrac{12}{30}}$ Subtract the whole numbers: $=12 + {\dfrac{35}{30}} - {\dfrac{12}{30}}$ Subtract the fractions: $= 12+\dfrac{23}{30}$ Combine the whole and fractional parts into a mixed number: $= 12\dfrac{23}{30}$